Question

factorise 4x²+9y²-25z²+12xy​

Answer 1

Answer:

( 2x + 3y + 5z ) ( 2x + 3y - 5z )

Step-by-step explanation:

Given----> 4x² + 9y² - 25z² + 12xy

To find---> Factors of given expression

Solution---> ATQ,

4x² + 9y² - 25 z² + 12xy

= ( 4x² + 9y² + 12xy ) - 25z²

= { ( 2x )² + ( 3y )² + 2 ( 2x ) ( 3y ) } - ( 5z )²

We know that,

( a + b )² = a² + b² + 2ab , applying it , we get,

= ( 2x + 3y )² - ( 5z )²

We know that ,

( a² - b² ) = ( a + b ) ( a - b ) , applying it , we get,

= ( 2x + 3y + 5z ) ( 2x + 3y - 5z )

Additional identities ----->

1) ( a - b )² = a² + b² - 2ab

2) ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

3) ( a + b )³ = a³ + b³ + 3ab ( a + b )

4) ( a - b )³ = a³ - b³ - 3ab ( a - b )

5) ( a³ + b³ ) = ( a + b ) ( a² + b² - ab )

6) ( a³ - b³ ) = ( a - b ) ( a² + b² + ab )